The influence of changing material or/and shape of packging on Naked juice: Test on targeted customers’ purchase intention
Hudson_express:Haotian Chi,Yumeng Fan,Margaret Ma,Ziyu Zhu,Xinyi Zhang
Part 1: Research Proposal
Executive Summary / Abstract
Authors (Sky 40%, Ziyu 60%):
The study will explore how packaging shapes and materials can have a profound impact on consumer preferences for Naked Juice, especially consumer’s purchase intent . Naked Juice is one of the popular brands of PepsiCo., but Center for Science in the Public Interest (CSPI) sued Naked Juice in 2016 for its misleading advertisement on the package. The ingredients include fruit concentration which leads people to question whether Naked Juice is that healthy as it seems on its ads. Thus, Naked Juice was forced to take down “100% natural” on all of its labels. It is urgent to help Naked Juice gain back consumer’s faith and like, despite the missing “100% natural” label. These challenges hold the key to a shift that will force the brand to reimagine its approach to a favorable representation and avoid potentially fraudulent labeling practices.
The core of this study is an exploration of the silent but persuasive descriptors of packaging - shape and material. The goal was to reveal how these non-verbal cues significantly adjust consumer behaviors. The main outcome variable in this study is consumer’s purchase intent (scaled 1 to 10). Using a robust Two-Way ANOVA methodology, the study was designed to strictly test the hypothesis that packaging in terms of material and shape affects key consumer metrics. Our two-way ANOVA involves two categorical independent variables which are shape and material and each of them has two levels. For example, the shape category includes rectangular and curved, material category includes plastic and glass. Naked Juice’s current package is composed of plastic and rectangular shape, so we explored the change of purchase intent brought by the new combinations of two categorical variables. Through our analysis and survey, we founded that changing the packaging from a rectangular shape to a curved shape slightly increased customer purchase intent for Naked Juice, but the effect was not as significant as changing the material.
Beyond simple analysis, the study also hopes to figure out the interplay of materials and shapes in packaging to determine if these subtle changes are effective in reshaping consumer behavior and perceptions. We already know that people dislike environmentally friendly plastic materials and people think round shape is related to sweetness according to the literature review. What we don’t know is how these perceptions will reflect in people’s purchase intent of juice. Essentially, this study is a strategic effort by Naked Juice to rebuild and strengthen a brand image that resonates with authenticity and wellness, refocusing its package descriptions to respond to the changing expectations and preferences of today’s consumers. The future study also includes the impact of package change on people’s perception of freshness and healthiness, elements that are critical to solidifying consumer trust and carving out a unique niche in the beverage industry’s competition landscape. This is more than a study, it’s a journey to redefine brand identity through packaging innovation.
Statement of the Problem
Authors (Sky 100%):
The Naked Juice was filed against its “all natural” statement on the label because some vitamins are synthesized which is considered not 100% natural. The Naked Juice was forced to take off “all natural” wordings on the drink packages. In 2016, the The Naked Juice’s label was filed again by the Center for Science in the Public Interest, stating its Kale Blazer juice’s label is all green which suggests the drink is made of green vegetables and healthy ingredients(Riddle, 2023). However, apple juice and orange are the main components of Kale Blazer, which is considered poor-nutrients and cheap. The Naked Juice is in need of strengthening its health image across its drink products by means other than tricking on the label phrasing. In this research, we will study the effect of the shape and material of the packages on consumer’s purchase choice and perception of The Naked Juice’s healthiness. Read More: https://www.mashed.com/626940/the-untold-truth-of-naked-juice/
What are the non-verbal factors contributing to the positive perception of bottled juices’ freshness and healthiness?
Literature Review
Material
Authors (Ziyu Zhu 100%):
In recent years, there has been an increasingly noticeable transition in consumer preferences for sustainable packaging, driven by increased environmental awareness. This transition is confirmed by Lindh et al. (2016), which utilize surveys and environmental impact assessments to measure consumer attitudes. They collected qualitative and quantitative data on consumer perceptions of food packaging through a combination of open-ended and closed-ended questions. This approach provides a comprehensive view to capture the nuances of consumer opinions and preferences. This study has shown that consumers prefer recyclable materials, such as glass and paper, over traditional plastics, mainly because of their lower environmental impact. Notably, Lindh et al. found that 62% of consumers consider plastic to be the most environmentally harmful packaging material, hence they prefer more sustainable alternatives.
The preference for glass packaging highlighted by Allegra et al. (2012) is particularly interesting. By collecting 326 questionnaires from retail stores in Eastern Sicily, Fishbein’s compensatory modeling approach was applied to define the competitive position of primary containers in consumer perception. Nearly two thirds of consumers (66.7%) favored glass packaging because of its recyclability, reusability, and product purity and quality. In contrast, only a small percentage preferred paper and only 9% opted for plastic. This trend reflects not only increased environmental awareness, but also a transition in consumer behavior and attitudes.These approaches offer the possibility of exploring how packaging materials influence consumers’ preferences, providing a comprehensive insight into the evolution of consumer preferences in the context of environmental sustainability.
Shape
Authors (Sky 100%): The research The perceived sweetness and price of bottled drinks’ silhouette written by Ana M.Arboleda and Carlos Arce-Lopera discusses if drink’s package shape can communicate intrinsic product character (taste) and extrinsic product character (price). The study used a chi-squared test to compare if different shapes will have different chosen frequency as “sweeter” or “pricer”. The result reveals a cross-model correspondence between taste and shape on drink’s packages, see Table 2 (Ana M. Arboleda a et al., 2019) People used to perceive drinks with round and voluminous packages sweeter, and sweetness perception is associated with calories content and obesity(Koo & Suk, 2016) which may affect consumer’s choice when purchasing a drink. On the other hand, curved bottles (more variance means more curvatures and details that change the continuous line of the silhouette) are associated with higher price and bitterness in consumer’s perceptions. However, the result is limited to specific categories of drinks so we need further research on packages’ physical characteristics impact on Naked Juice.
Research Questions, Hypotheses, and Effects
Authors (Xinyi Zhang 100%):
Research question:
Relative to the original shape and material design of Naked products, is the change of material or shape or both of them will lead to any difference for customers’ purchase intentions?
1.Questions about main effects: Does change of material packaging affect customers’ purchase intentions? Does change of shape packaging affect customers’ purchase intentions? 2.Questions about interaction effects: Does the combination of material and shape packaging lead to different customers’ purchase intentions compared to only one or neither of these packaging features is present?
Hypothesis:
Metric: average score of collected participants’ responses regarding their frequency for purchase Naked product, scale of score :1-10
Threshold: α=5% P-value less than the threshold value leads us to reject the null hypothesis
Two-way anova: inherently two-sided tests , compare any differences among group means
Independent variable: (treatment group) 1.glass material packaging (glass_rectangular) 2. curve shaped packaging (plastic_curve) 3. interaction: glass material and curve shaped packaging(glass_curve) (control group) 1.original packaging(plastic_rectangular)
Dependent variable: Customers’ purchase intention
Null hypothesis(H0): 1.There is no effect of the glass material packaging on customers’ purchase intention. 𝜇original = 𝜇glass_rectangular 2. There is no effect of the curved shaped packaging on customers’ purchase intention. 𝜇original=𝜇plastic_curve 3. There is no interaction effect between glass packaging and curve shaped packaging on customers’ purchase intention. 𝜇original =𝜇_glass_curve
Alternative hypothesis(HA): 1. There is an effect of the glass material packaging on customers’ purchase intention. 𝜇original ≠ 𝜇glass_rectangular 2. There is an effect of the curved shaped packaging on customers’ purchase intention. 𝜇original ≠ 𝜇plastic_curve 3. There is an interaction effect between glass material packaging and curve shaped packaging on customers’ purchase intention. 𝜇original ≠ 𝜇_glass_curve
Effect size: We use eta squared η2 as effect size, η2=SSB/SST. SSB is the variation caused by treatment, and SST is the variation of Treatment + Noise. η2 explains how much each variable explain the whole variance. We simulate 10,000 times of 127 purchase intent score results for each of the four combinations and set the mean effect size from the 10,000 times simulation as the effect size η2. The more time we simulate, the more unbiased effect size we can get.
After running 10,000 times of simulation, we get the benchmark effect
size as follow:
The mean partial eta squared for material is 0.010. The partial eta
squared for shape is 0.025. The partial eta squared for material is
0.003.
Effects: Change of packaging material from plastic to glass could influence customers’ choices on Naked products. Customers are likely to increase their frequency of purchase with Naked products.
By designing new packaging like fruit-shaped bottles could generate customers with more interest to buy Naked products while rooting a healthy image in their head that Naked juice is fresh made of fruit as the bottle shaped. Hence, this connection further improves Naked company’s power or brand value among the juice beverage companies which could finally help improve Naked company’s products sales and thus revenues.
Packaging changes could help expand the customer group. While we switch from plastic to glass, customers who pay specific attention to the packaging environmental issues would likely choose our product as plastic is not eco-friendly while glass could be recycled. In addition, the change of bottle to fruit-shape could be popular among younger generations which further extend our customer group range.
Research Plan
Population of Interest
Authors (Yumeng Fan 100%): Naked Juice provides a variety of juice beverages with a range of flavors, often incorporating natural ingredients like vegetables, fruits, and other organic components. Naked Juice is committed to never including artificial flavors, preservatives, or extra sugars in its offerings. Additionally, Naked Juice positions itself as a health-focused brand, with its products often containing substantial levels of essential vitamins and nutrients. They also incorporate green tea extract and Guarana for natural caffeine content. Each of their beverages provides 100 percent of the recommended daily intake (RDI) for a specific vitamin. The majority of Naked Juice’s products are also suitable for vegans, as they do not contain any ingredients or processing aids sourced from; produced, or processed by animals. This aligns well with the preferences of vegan and vegetarian consumers.
We chose Naked Juice’s target customers as our population of interest.
Health-conscious individuals:
Naked Juice emphasizes natural ingredients and doesn’t add any sugar, flavors, or preservatives, health-conscious consumers are likely to buy Naked Juice. These people prioritize nutritious and healthy foods and beverages, and they may be looking for convenient ways to increase their daily intake of vitamins and antioxidants.
Active and busy consumers:
Naked Juice contains green tea extract and natural caffeine from Guarana, suggesting they are targeting consumers who live an active lifestyle and need a boost of energy during the day. This could cover a wide range of individuals, such as students and professionals with busy schedules. These customers may like the convenience of Naked Juice products because it can provide them with adequate hydration, energy, and nutrients.
Vegetarians:
Most of Naked Juice’s products are suitable for vegetarians since they eliminate all animal-derived ingredients from their diet, including meat, poultry, fish, dairy, eggs, and any other animal by-products. Ingredients produced or processed by animals are also excluded. These include ingredients such as gelatin, animal enzymes, sugar refined from animal bone char, and honey. This resonates with consumers looking for plant-based, cruelty-free, and ethically conscious beverage options.
Sample Selection
Authors (Yumeng Fan 100%):
Random sampling:
The research team plans to randomly select one supermarket (e.g., Target) selling Naked Juice in each region across the United States (the Northeast, the Midwest, the South, and the West) as a testing store. From each testing store, participants passing a specific point in a designated aisle will be randomly selected and given a preliminary questionnaire, asking if they identify as either a health-conscious individual, an active and busy consumer, or a vegetarian. Participants who identify as at least one of these target customer segments will proceed to the actual research process. The goal is to collect a minimum of 128 questionnaires in each testing store, resulting in a total of at least 512 valid results.
Operational Procedures
Authors (Margaret Ma 100%):
Research Setting and Time Frame
The research will be conducted in four Target stores each randomly selected from each region (West, South, Midwest, Northeast) in the United States. The study period spans from January 1st to Feb 4st, 2024, with research activities scheduled from Monday to Sunday, 10am to 8pm. This schedule ensures comprehensive coverage of different shopping patterns and behaviors throughout the week.
Participants and Data Collection Team
Participants in this study will consist of Target shoppers who pass a specific point in the Juice Aisle and self-identify as our target customers via the preliminary customer segmentation questionnaire. Eligible participants must have an intermediate level of English proficiency to understand and respond to the questionnaire and possess adequate eyesight to view the displayed pictures. The study will exclude children under 18 years old.
The data collection team will be composed of members from the marketing department of Naked Juice. This study requires a total of eight data collectors, with two assigned to each Target store. These collectors will work in shifts to ensure compliance with legal working hours.
Researchers Training and Monitoring
The training for researchers will focus on ensuring non-interference with participants’ survey responses. Training will provide a clear definition of each questionnaire item, equipping researchers with the necessary knowledge to explain any unclear items to participants without influencing their responses. In addition, standard data collection procedures will be taught, along with conducting mock trials to prepare for various scenarios. These scenarios include participants choosing not to finish the survey before submission and those providing random answers. In the case of incomplete surveys, researchers should not submit these and must erase any partially filled records. However, for surveys with seemingly random answers, researchers should submit the results as usual, considering that such responses could occur across all four groups.
To maintain adherence to the protocol, two researchers at each site will monitor each other’s compliance, supplemented by regular check-ins from research managers.
Manner to Interact with Subjects
The general information about the research will be communicated to potential participants by the data collectors. They will introduce themselves as members of the Research Team for Naked Juice and explain the study’s objective: to assess how changes in bottling affect customers’ willingness to purchase and their perception of the juice. Participants will be informed about the reward (a bottle of Naked Juice) for completing the study, the estimated two-minute duration of the survey, the general procedures, and the assurance that no sensitive information will be collected. Researchers will clarify that the reward is unrelated to specific survey responses and to encourage participants to provide honest feedback. If participants consent, data collectors will follow the steps listed in the data collection section.
Participation Bias
The study acknowledges potential participation biases. Enthusiasts of Naked Juice or those in a good mood and not in a hurry may be more inclined to participate. Conversely, busy customers or those indifferent to juice may choose not to participate. This bias will be considered as one of the limitation.
Brief Schedule
Authors (Margaret Ma 100%):
Step One: Collaboration and Preparation
The first step involves collaborating with Naked Juice to ensure the smooth execution of the research project. Our research team will leverage their partnership with Target to secure Target’s support as the testing market and randomly select one Target store from each region as the testing store. Additionally, Naked Juice will provide necessary support for designing the bottle images used during the testing period and supplying the required electronic devices and reward, such as iPad and Naked juice, for the research project. Additionally, the training program for data collectors will be conducted during this stage.(Timeline: 01/01/2024 - 01/14/2024)
Step Two: Image and Questionnaire Design
The second step involves designing the digital images for presentation during the testing period and creating both the preliminary customer segmentation questionnaire and survey questionnaires with relevant questions of interest. Multiple tests should be conducted to ensure that the Google Form functions properly. (Timeline: 01/01/2024 - 01/14/2024)
Step Three: Data Collection
The third step focuses on presenting the images and collecting data. Eight data collectors will be assigned to the four testing sites to facilitate the data collection. At each Target location, the objective is to gather a minimum of 128 valid responses, with each group (including one control group and three treatment groups) providing at least 32 responses.(Timeline: 01/15/2024 - 01/21/2024)
Step Four: Statistical Analysis
The forth step is dedicated to statistical analysis. The research team will consolidate data from the four testing stores and calculate the average perception scores for each dependent variables in every group. Two way ANOVA Test will be conducted to assess statistically significant differences. (Timeline: 01/22/2024 - 01/28/2024)
Step Five: Report Inferences and Recommendation
The fifth step involves drawing inferences and providing recommendations. Depending on the statistical results, the research team will determine whether the material and shape of the juice bottle will influence people’s purchasing intentions and perceptions of the juice. Additionally, by evaluating the effect size, the team will assess if the difference is substantial enough to create a meaningful impact on sales and business performance, and whether the improvement will outweigh the initial investment required for changing the packaging. (Timeline: 01/22/2024 - 02/04/2024)
Data Collection
Authors (Margaret Ma 100%): The data collection process consists of two steps:
Initial Questionnaire: Participants who consent to participate will first complete a preliminary customer segmentation self-identification questionnaire on an iPad. This questionnaire helps to determine if they are part of our target customer group. If a participant matches at least one of our three target groups, they will proceed to the second step of the data collection process.
Follow-up Survey: For participants identified as target customers, the conductor will randomly assign them to one of the study groups using Excel’s random function (RANDBETWEEN(0,3)). Subsequently, participants will view a bottle picture corresponding to their assigned group and complete a Purchase Intention & Perception Survey on the iPad. The data collected will include their unique ID, customer segmentation identity, survey group code, and survey responses regarding purchase intention and perception. Finally, each completed questionnaire will be uploaded to our record system.
Data Security
Authors (Margaret Ma 100%): Training on data confidentiality will be provided to all researchers before the research. All participants should be identified with an ID code instead of their legal names, and all raw data will be stored within Naked Juice’s company-secured system.
Variables
Outcomes (Dependent Variables)
Authors (Margaret Ma 100%): The outcome of this survey will include the purchase intention score for the juice. This score serves as a direct measurement of how packaging influences people’s purchasing behavior, potentially impacting our sales.
Treatments (Independent Variables)
Authors (Margaret Ma 100%): There are three treatment groups: rectangular shape glass material, curve shape plastic material,, and curve shape glass material, in addition to the control group, which uses the original rectangular plastic bottle.
In the rectangular_glass (Treatment 1) treatment group, all other factors will remain unchanged, with only the material transitioning from plastic to glass, allowing us to assess the impact of the material change alone. In the curve_plastic (Treatment 2) treatment group, the only modification from the control group is the alteration in shape, enabling us to isolate the effects of the shape change. In the curve_glass (Treatment 3) treatment group, both the material and shape are altered to determine whether this combination has an additional impact on purchase intention and perception. The treatment information will be presented to participants in the form of digital images on an iPad for cost-efficiency reasons.
Other Variables
Authors (Margaret Ma 100%): In addition to the purchase intention score, this survey will also collect perception scores related to healthiness, freshness, deliciousness, convenience, the addition of sugar & artificial flavors, and the brand’s commitment to sustainability. These six features represent the core values of Naked Juice, and the brand hopes customers recognize these as indicative of ‘goodness inside our products’ and our efforts to ‘bring goodness to the world’ through sustainable materials. These perception scores will serve as direct, measurable criteria for evaluating how different packaging options enhance our image in line with our intentions.
Furthermore, the customer segmentation data gathered through the survey could, in the future, be used to delve deeper, potentially drawing inferences about variations in purchase intentions and perceptions across different customer groups.
Statistical Analysis Plan
Authors (Xinyi Zhang 100%):
Our group chose to use two-way anova as our statistical test to use in our designed experiment. After simulation of data, we decided to use linear regression model first for our three terms: material, shape and one interaction term: material * shape. Then we will use the anova test function for analysis and also to extract the eta-square and p-value for material, shape and material*shape. After creating the analysis function, we will simulate data for 1000 times and repeat the analysis 1000 times. Then, we will use t-test to calculate the mean and confidence interval for simulated eta-squares. Based on the statistics we had, we could know if our chosen independent variables are significant or not. In addition, we will analyze the type 1 and type 2 error to see if the result meets with our previous assumptions and to see what suggestions our design of experiment could offer to Naked juice company for their later design of product: Should they change the material of packaging or shape of packaging or both.
Sample Size and Statistical Power
Authors (Sky 70% Xinyi Zhang 30%):
For the sample size calculation, we used one-way anova test for material group and shape group separately, setting the test power at 0.8 and significant level at 0.05.
We assume the mean score for the original package (rectangular and plastic) is 5, the mean score for curve package (curve and plastic) is 5.75, and the mean score for glass package (rectangular and glass) is 5.5. According to the research article[1], it is appropriate to set mean standard deviation equal to 2. We performed the sample size calculation as following:
Code: pwr.anova.test(k = 2 , f = ((5.5-5)/2)/2, #f = (mean difference-mean standard deviation)/2 sig.level = 0.05, power=0.8)#Material sample size
N=253. The sample size we get from the above calculation is for material group, so each material group (plastic and glass) will need the sample size n/2, which is 127 sample needed per group.
We did the same for shape group’s sample size:
Code: pwr.anova.test(k = 2 , f = ((5.75-5)/2)/2, #cohen’s f = (mean difference-mean standard deviation)/2 sig.level = 0.05, power=0.8)#shape sample size
N=113, which means each shape group (rectangular and curve) will each need 57 sample. Overall, we need at least 127 each group since we are doing the two-way anova test that shape and material will interact together. Thus, we need 508 samples in total, which is 127*4, to ensure meet the power and significance level.
Possible Recommendations
Authors (Yumeng Fan 100%):
Does change of material packaging affect customers’ purchase intentions? the null hypothesis is not rejected This would indicate that a change in material packaging would not significantly affect a customer’s intention to buy. Recommendations can focus on maintaining current packaging materials, as changing them may not lead to increased sales or customer interest. Resources can be better allocated to other aspects of product development or marketing strategies that have a more direct impact on customer preferences.
the null hypothesis is rejected This indicates that a change in material packaging can significantly affect a customer’s purchase intention. Proposals will include exploring new and innovative packaging materials in line with customer preferences, environmental considerations and brand image. This may involve investing in market research to understand which materials resonate best with your target audience and developing strategies to effectively implement these changes.
Does change of shape packaging affect customers’ purchase intentions? the null hypothesis is not rejected If the package shape has no significant effect on purchase intention, it is recommended to maintain the current shape of the package. Efforts and investments can be redirected to other areas, such as product quality, pricing strategies, or promotions, which may have a more pronounced impact on purchase intentions.
the null hypothesis is rejected If the change in the package shape significantly affects the purchase intention, it is recommended to try a different package shape that can attract consumers. This may involve creative and innovative design that differentiates the products on the shelves, potentially increasing customer appeal and purchase volume.
Does the combination of material and shape packaging lead to different customers’ purchase intentions compared to only one or neither of these packaging features is present? the null hypothesis is not rejected This result implies that the combination of packaging material and shape has no significant interaction with purchase intention. Recommendations could focus on addressing these factors individually, rather than investing in combining them. It may be more beneficial to determine which single factor (material or shape) has a greater impact and focus on that.
the null hypothesis is rejected If the interaction between the material and the shape is significant, this indicates that it is a synergistic effect, and the combination of these factors affects the customer’s purchase intention more than one factor alone. Recommendations will involve developing packaging that strategically combines these two elements to maximize customer appeal. This may include detailed consumer research to determine the most effective combinations and innovative design approaches.
Limitations and Uncertainties
Authors (Ziyu Zhu100%):
When conducting research to assess the impact of packaging changes on consumer perceptions and purchase intentions of naked fruit juice, it is of utmost importance to recognize and address the inherent limitations and uncertainties that may affect the results of the survey. One of the most critical aspects to consider is the representativeness of the sample used in the survey. The demographic diversity of the sample, including factors such as gender, geographic location, and income level, plays an important role in determining the validity and suitability of the outcome of the survey. The potential lack of representation of certain customer groups in the survey may limit the generalizability of the outcomes, making it challenging to apply the findings to a broader and more diverse group of consumers.
The psychological factors such as brand loyalty and perceived benefits are other key factors that add to the complexity of understanding consumer behavior. Individual consumer preferences can vary widely and are influenced by a variety of factors that are often difficult to quantify or control for in a research setting. This variability can make it challenging to accurately predict consumer responses to packaging changes. In addition, external economic conditions, including competitor behavior and broader market conditions, may have a significant impact on consumer perceptions and behavior. These external factors may bias the research, potentially biasing the outcomes and limiting their relevance to real-world market scenarios.
Another major obstacle to research on packaging changes is the difficulty of measuring the long-term impact of these changes on consumer behavior. Consumer preferences and attitudes are not static; they evolve over time and are influenced by current market trends and societal changes. Short-term studies may fail to capture these dynamic aspects, leading to uncertainty about the long-term impact of packaging changes. This uncertainty is a great challenge for researchers, as it complicates the ability to draw definitive conclusions about the effectiveness and sustainability of packaging modifications.
Finally, the research’s reliance on Two-Way ANOVA, while a reliable statistical method, introduces interpretive complexity, especially when dealing with interaction effects. The fact that the impact of one packaging change may depend on the likelihood of another packaging change complicates the analysis. This complexity is further exacerbated when considering how packaging changes interact with other marketing elements such as advertising, product placement and pricing strategies. In addition, the findings have limited potential replicability across different markets or products, narrowing their applicability. Addressing these multifaceted challenges requires a comprehensive study design, in-depth data analysis, and careful interpretation of the results. Such an approach should take into account the dynamic nature of consumer behaviour and market conditions, as well as the possible impact of unmeasured variables, in order to enhance the robustness and generalizability of the findings.
Part 2: Simulated Studies
Authors (Xinyi Zhang 100%):
# If your research questions are part of a single experiment, then simulate your data here.
library(data.table);library(DT)
set.seed(seed=4172)
n<-508
one.dat<-data.table(Group= c(rep.int(x="rectangular_glass",times = n/4),rep.int( x = "rectangular_plastic",times = n/4),rep.int( x = "curve_glass",times = n/4),rep.int( x = "curve_plastic",times = n/4)))
one.dat[Group == "rectangular_plastic",score:= round(x=rnorm(n=.N,mean=5,sd=2),digits = 1)]
one.dat[Group == "rectangular_glass",score:= round(x=rnorm(n=.N,mean=5.5,sd=2),digits = 1)]
one.dat[Group == "curve_plastic",score:= round(x=rnorm(n=.N,mean=5.75,sd=2),digits = 1)]
one.dat[Group == "curve_glass",score:= round(x=rnorm(n=.N,mean=6,sd=2),digits = 1)]
one.dat[Group == "curve_glass",shape:= "curve"]
one.dat[Group == "curve_glass",material:= "glass"]
one.dat[Group == "curve_plastic",shape:= "curve"]
one.dat[Group == "curve_plastic",material:= "plastic"]
one.dat[Group == "rectangular_glass",shape:= "rectangular"]
one.dat[Group == "rectangular_glass",material:= "glass"]
one.dat[Group == "rectangular_plastic",shape:= "rectangular"]
one.dat[Group == "rectangular_plastic",material:= "plastic"]
datatable(data=one.dat)dim(one.dat)[1] 508 4#analysis function to perform ANOVA tests
analyze.experiment <- function(the.dat) {
require(data.table)
setDT(the.dat)
#fit two way anova test model
model<-lm(score~material+shape+material*shape, dat=the.dat)
#extract model summary
anova_summary<-anova(model)
#extract coefficients and construct result
material.ss<-anova_summary$`Sum Sq`[1]
shape.ss<-anova_summary$`Sum Sq`[2]
interact.ss<-anova_summary$`Sum Sq`[3]
p.material<-anova_summary$`Pr(>F)`[1]
p.shape<-anova_summary$`Pr(>F)`[2]
p.interact<-anova_summary$`Pr(>F)`[3]
eta.squares.material<- anova_summary$`Sum Sq`[1]/(anova_summary$`Sum Sq`[1] + anova_summary$`Sum Sq`[2] +anova_summary$`Sum Sq`[3]+ anova_summary$`Sum Sq`[4])
eta.squares.shape<- anova_summary$`Sum Sq`[2]/(anova_summary$`Sum Sq`[1] + anova_summary$`Sum Sq`[2] +anova_summary$`Sum Sq`[3]+ anova_summary$`Sum Sq`[4])
eta.squares.material.shape<- anova_summary$`Sum Sq`[3]/(anova_summary$`Sum Sq`[1] + anova_summary$`Sum Sq`[2] +anova_summary$`Sum Sq`[3]+ anova_summary$`Sum Sq`[4])
result<- data.table(material_variation = material.ss,
shape_variation =shape.ss,
material_shape_variation=interact.ss,
p.material = p.material,
p.shape = p.shape,
p.interaction=p.interact,
material_effect = eta.squares.material,
shape_effect = eta.squares.shape,
interaction_effect = eta.squares.material.shape)
return(result)
}
analyze.experiment(the.dat=one.dat) material_variation shape_variation material_shape_variation p.material
1: 1.610157 59.18811 9.700866 0.5497657
p.shape p.interaction material_effect shape_effect interaction_effect
1: 0.0003138419 0.1424348 0.000689302 0.02533819 0.004152902# Run 1000 experiment
B<-1000
n<-508
RNGversion(vstr=3.6)
set.seed(seed=4172)
Experiment<-1:B
Group<- c(rep.int(x="rectangular_glass",times = n/4),rep.int( x = "rectangular_plastic",times = n/4),rep.int( x = "curve_glass",times = n/4),rep.int( x = "curve_plastic",times = n/4))
library(data.table)
sim.dat<- as.data.table(expand.grid(Experiment = Experiment, Group = Group))
setorder(sim.dat, cols = "Experiment")
sim.dat[Group == "rectangular_plastic",score:= round(x=rnorm(n=.N,mean=5,sd=2),digits = 1)]
sim.dat[Group == "rectangular_glass",score:= round(x=rnorm(n=.N,mean=5.5,sd=2),digits = 1)]
sim.dat[Group == "curve_plastic",score:= round(x=rnorm(n=.N,mean=5.75,sd=2),digits = 1)]
sim.dat[Group == "curve_glass",score:= round(x=rnorm(n=.N,mean=6,sd=2),digits = 1)]
sim.dat[Group == "curve_glass",shape:= "curve"]
sim.dat[Group == "curve_glass",material:= "glass"]
sim.dat[Group == "curve_plastic",shape:= "curve"]
sim.dat[Group == "curve_plastic",material:= "plastic"]
sim.dat[Group == "rectangular_glass",shape:= "rectangular"]
sim.dat[Group == "rectangular_glass",material:= "glass"]
sim.dat[Group == "rectangular_plastic",shape:= "rectangular"]
sim.dat[Group == "rectangular_plastic",material:= "plastic"]
dim(sim.dat)[1] 508000 5exp.results<- sim.dat[,analyze.experiment(the.dat = .SD),keyby = "Experiment"]
exp.results Experiment material_variation shape_variation material_shape_variation
1: 1 6.553720 89.560807 0.523011811
2: 2 23.430728 99.744114 4.329940945
3: 3 21.291339 70.168189 0.002834646
4: 4 14.933878 116.142539 19.176555118
5: 5 9.372047 56.889764 6.576456693
---
996: 996 10.955039 120.485748 26.396929134
997: 997 9.075610 82.162382 7.015925197
998: 998 39.804803 66.067402 7.324803150
999: 999 63.567106 66.573248 6.690728346
1000: 1000 31.600177 6.829154 1.087106299
p.material p.shape p.interaction material_effect shape_effect
1: 2.101228e-01 4.473758e-06 0.72312490 0.002986606 0.040813896
2: 1.511140e-02 6.822337e-07 0.29510914 0.011082515 0.047178030
3: 2.817459e-02 7.403236e-05 0.97974721 0.009232359 0.030426358
4: 5.242294e-02 9.157819e-08 0.02803441 0.006973863 0.054236560
5: 1.148815e-01 1.131549e-04 0.18643602 0.004765832 0.028929332
---
996: 1.064024e-01 1.241937e-07 0.01235893 0.004829685 0.053117860
997: 1.191749e-01 3.417311e-06 0.17055027 0.004593734 0.041587523
998: 1.668549e-03 5.411319e-05 0.17575172 0.018763834 0.031143924
999: 4.573147e-05 3.044633e-05 0.18275286 0.031293906 0.032773821
1000: 4.279969e-03 1.827730e-01 0.59476552 0.016013450 0.003460687
interaction_effect
1: 2.383425e-04
2: 2.048021e-03
3: 1.229160e-06
4: 8.955120e-03
5: 3.344231e-03
---
996: 1.163746e-02
997: 3.551199e-03
998: 3.452885e-03
999: 3.293827e-03
1000: 5.508932e-04#Extract eta for 1000 experiment
material_eta <- exp.results$material_effect
shape_eta <- exp.results$shape_effect
interaction_eta <- exp.results$interaction_effect
#t test to extract mean,95%confidence interval, p-value
analyze_eta_squared <- function(material_eta, shape_eta, interaction_eta) {
# Conduct t-tests
t_test_material <- t.test(material_eta)
t_test_shape <- t.test(shape_eta)
t_test_interaction <- t.test(interaction_eta)
# Extract statistics
results <- data.frame(
effect = c("Material", "Shape", "Interaction"),
mean_effect_size = c(t_test_material$estimate, t_test_shape$estimate, t_test_interaction$estimate),
lower_conf_int = c(t_test_material$conf.int[1], t_test_shape$conf.int[1], t_test_interaction$conf.int[1]),
upper_conf_int = c(t_test_material$conf.int[2], t_test_shape$conf.int[2], t_test_interaction$conf.int[2]),
p_value = c(t_test_material$p.value, t_test_shape$p.value, t_test_interaction$p.value)
)
return(results)
}
# t-test result table
results_table <- analyze_eta_squared(material_eta, shape_eta, interaction_eta)
results_table effect mean_effect_size lower_conf_int upper_conf_int p_value
1 Material 0.010409544 0.009867701 0.010951388 3.663393e-194
2 Shape 0.025560279 0.024716738 0.026403821 0.000000e+00
3 Interaction 0.002982909 0.002741385 0.003224432 1.987983e-102Benchmark eta
#Though anova test only test two sided for has effect or not, in order to give suggestions for the company we decided to set up a benchmark #Calculated through eta-squares after running 10,000 times analysis to decrease the possiblity of bias #Set up a Benchmark smaller or equal than the benchmark: no effect, greater than the benchmark: has effect Authors (Sky 100%):
anova=aov(score~ shape * material,data=one.dat)
summary(one.dat) Group score shape material
Length:508 Min. :-1.000 Length:508 Length:508
Class :character 1st Qu.: 3.900 Class :character Class :character
Mode :character Median : 5.400 Mode :character Mode :character
Mean : 5.459
3rd Qu.: 6.900
Max. :11.700 η2_material=0.010243924
η2_shape= 0.025410512
η2_interaction=0.002835907True effect of each scenario
Authors (Xinyi Zhang 100%):
library(dplyr)
# Research question 1
# No effect
no_effect_material <- exp.results %>%
filter(material_effect <= η2_material) %>%
summarize(mean_effect_size = mean(material_effect)) %>%
mutate(question = "Research question 1", effect_presence = "No effect")
# Has effect
has_effect_material <- exp.results %>%
filter(material_effect > η2_material) %>%
summarize(mean_effect_size = mean(material_effect)) %>%
mutate(question = "Research question 1", effect_presence = "Has effect")
# Research question 2
# No effect
no_effect_shape <- exp.results %>%
filter(shape_effect <= η2_shape) %>%
summarize(mean_effect_size = mean(shape_effect)) %>%
mutate(question = "Research question 2", effect_presence = "No effect")
# Has effect
has_effect_shape <- exp.results %>%
filter(shape_effect > η2_shape) %>%
summarize(mean_effect_size = mean(shape_effect)) %>%
mutate(question = "Research question 2", effect_presence = "Has effect")
# Research question 3
# No effect
no_effect_interaction <- exp.results %>%
filter(interaction_effect <= η2_interaction) %>%
summarize(mean_effect_size = mean(interaction_effect)) %>%
mutate(question = "Research question 3", effect_presence = "No effect")
# Has effect
has_effect_interaction <- exp.results %>%
filter(interaction_effect > η2_interaction) %>%
summarize(mean_effect_size = mean(interaction_effect)) %>%
mutate(question = "Research question 3", effect_presence = "Has effect")
# Combine all results into one table
combined_results <- rbind(no_effect_material, has_effect_material,
no_effect_shape, has_effect_shape,
no_effect_interaction, has_effect_interaction)
# View the combined results
combined_results mean_effect_size question effect_presence
1 0.0049476948 Research question 1 No effect
2 0.0187751620 Research question 1 Has effect
3 0.0156566161 Research question 2 No effect
4 0.0374708525 Research question 2 Has effect
5 0.0008166879 Research question 3 No effect
6 0.0068675838 Research question 3 Has effectResearch Question 1: Does change of material packaging affect customers’ purchase intentions?
Scenario 1: No Effect
Authors (Sky 50% Xinyi Zhang 50%):
Analysis
exp.results$material_effect=ifelse(exp.results$material_effect <= η2_material, 0, 1)
1-(sum(exp.results$material_effect)/1000)#no effect[1] 0.605library(dplyr)
#H0=true, reject H0. (Type I)
error1_material=exp.results%>%filter(material_effect==0)%>%summarize(error1_material=sum(p.material<=0.05))
#H0=true, does not reject H0. (TN)
TN_material=exp.results%>%filter(material_effect==0)%>%summarize(TN_material=sum(p.material>0.05))Scenario 2: An Expected Effect
Authors (Sky 50% Xinyi Zhang 50%):
Analysis
#95% confidence interval
results_table$lower_conf_int[1] #lower_conf_int[1] 0.009867701results_table$upper_conf_int[1]#upper_conf_int[1] 0.01095139exp.results$material_effect=ifelse(exp.results$material_effect <= η2_material, 0, 1)
sum(exp.results$material_effect)/1000#has effect[1] 0.395library(dplyr)
#H0=false, reject H0. (Type II)
error2_material=exp.results%>%filter(material_effect==1)%>%summarize(error2_material=sum(p.material<=0.05))
#H0=false, does not reject H0. (TP)
TP_material=exp.results%>%filter(material_effect==1)%>%summarize(TP_material=sum(p.material>0.05))Research Question 2:Does change of shape packaging affect customers’ purchase intentions?
Scenario 1: No Effect
Authors (Sky 50% Xinyi Zhang 50%):
Analysis
exp.results$shape_effect=ifelse(exp.results$shape_effect <= η2_shape, 0, 1)
1-(sum(exp.results$shape_effect)/1000)#no effect[1] 0.546library(dplyr)
#H0=true, reject H0. (Type I)
error1_shape=exp.results%>%filter(shape_effect==0)%>%summarize(error1_material=sum(p.shape<=0.05))
#H0=true, does not reject H0. (TN)
TN_shape=exp.results%>%filter(shape_effect==0)%>%summarize(TN_shape=sum(p.shape>0.05))Scenario 2: An Expected Effect
Authors (Sky 50% Xinyi Zhang 50%):
Analysis
#95% confidence interval
results_table$lower_conf_int[2] #lower_conf_int[1] 0.02471674results_table$upper_conf_int[2]#upper_conf_int[1] 0.02640382exp.results$shape_effect=ifelse(exp.results$shape_effect <= η2_shape, 0, 1)
sum(exp.results$shape_effect)/1000#has effect[1] 0.454library(dplyr)
#H0=false, reject H0. (Type II)
error2_shape=exp.results%>%filter(shape_effect==1)%>%summarize(error2_shape=sum(p.shape<=0.05))
#H0=false, does not reject H0. (TP)
TP_shape=exp.results%>%filter(shape_effect==1)%>%summarize(TP_material=sum(p.shape>0.05))Research Question 3:Does the combination of material and shape packaging lead to different customers’ purchase intentions compared to only one or neither of these packaging features is present?
Scenario 1: No Effect
Authors (Sky 50% Xinyi Zhang 50%):
Analysis
exp.results$interaction_effect=ifelse(exp.results$interaction_effect <= η2_interaction, 0, 1)
1-(sum(exp.results$interaction_effect)/1000)#no effect[1] 0.642library(dplyr)
#H0=true, reject H0. (Type I)
error1_interaction=exp.results%>%filter(interaction_effect==0)%>%summarize(error1_interaction=sum(p.interaction<=0.05))
#H0=true, does not reject H0. (TN)
TN_interaction=exp.results%>%filter(interaction_effect==0)%>%summarize(TN_interaction=sum(p.interaction>0.05))Scenario 2: An Expected Effect
Authors (Sky 50% Xinyi Zhang50%):
Analysis
#95% confidence interval
results_table$lower_conf_int[3] #lower_conf_int[1] 0.002741385results_table$upper_conf_int[3]#upper_conf_int[1] 0.003224432exp.results$interaction_effect=ifelse(exp.results$interaction_effect <= η2_interaction, 0, 1)
sum(exp.results$interaction_effect)/1000#has effect[1] 0.358library(dplyr)
#H0=false, reject H0. (Type II)
error2_interaction=exp.results%>%filter(interaction_effect==1)%>%summarize(error2_interaction=sum(p.interaction<=0.05))
#H0=false, does not reject H0. (TP)
TP_interaction=exp.results%>%filter(interaction_effect==1)%>%summarize(TP_interaction=sum(p.interaction>0.05))Results table
Authors (Sky 50% Xinyi Zhang50%):
Results tables interpretations
Authors (Sky 100%):
From the advanced confusion table above, we can tell that changing a package into a combination of glass and curve together is likely to gain the expected effect size 0.003. However, this effect is too small to make an impact on Naked Juice’s purchase intent. It means that the interaction package change only explains 0.3% variance of the total purchase intent. On the other hand, we notice from the confusion table that changing material to glass or changing shape to curved does not hit our benchmark effect size often. This can be caused by the benchmark effect size being too big, plus we used a very strict way to define the true positive and true negative. For example, when the effect size is greater than the beach mark effect size, we say the scenario has the effect, and it will be concluded as true positive when the “has effect” scenario’s p value is less than 0.05 (reject H0).In comparing material’s and shape’s confusion table, material’s has 60.5% of the time has effect whereas shape only gas 45.4% of the time has effect. Thus, we decided to move forward with changing the material since the effect size 1% is an acceptable value to stimulate purchase intent (other residual factors are awaiting to explore to explain more variance of the purchase intent). Moreover, we have to further discuss different material’s impact on purchase intent scoring as well as other outcome variables such as healthiness, freshness, and deliciousness to get a comprehensive understanding of which factor contributes the most positive impact on Naked Juice brand image and sales demand.
References
Authors (Ziyu Zhu 80% Xinyi Zhang20%):
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H. Lindh, A. Olsson, H. Williams. (2016). Consumer perceptions of food packaging: contributing to or counteracting environmentally sustainable development? https://onlinelibrary.wiley.com/doi/full/10.1002/pts.2184?casa_token=cYmcGhYHLbkAAAAA%3AvLIFDKXsZKDjaiwwy3vct0Bem2soNGu1QW79lBcNoRLBTAzYCljQz4DCdSQZgQNYgJ8k2NsTtDNe7oX
Jieun Koo a et al. (2016).The effect of package shape on calorie estimation, International Journal of Research in Marketing. https://www.sciencedirect.com/science/article/pii/S0167811616300350
Sauro, J. (2020, January 21). Rating Scale Standard Deviations. MeasuringU. https://measuringu.com/rating-scale-standard-deviations/
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